Finite Group Databasebeta

← #14644682

Subgroups — #14644682

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2C2×#10622176C212yesmaximal
3#13066843C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C4×C11×C22⋊Q8C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11C411yescharacteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C11×#391C411yescharacteristic, complemented
10C11×#389C411yescharacteristic, complemented
11C11×#387—21no—
12C11×#385—21no—
13C11×#380C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C4×C11⋊C8—21no—
22#10622176C418yescomplemented
23#10622162—21no—
24C22×Q8×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8C2×C414yes—
31C4×Q8×C11—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11—42no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C22×C11⋊C8—22no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11⋊#95—22no—
54C11⋊#95—42no—
55C11⋊#95—42no—
56C11⋊#95C2×C414yes—
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)C2×C414yes—
59C4×C11⋊C8—42no—
60#8221—111nomaximal, Sylow
61C24×C11C2×D411yescharacteristic
62C2×Q8×C11—21no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11C4212yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11SD1612yes—
82C22×C4×C11Q1612yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4112yes—
87C22×Dic11—24no—
88C22×Dic11—42no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4C4212yes—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—42no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11—42no—
108C42×C11—42no—
109C2×C11⋊C8—24no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—42no—
112C4×C22⋊Q8D1111yescharacteristic
113C4×C22⋊C8—111no—
114C2×#328—112no—
115#1434—111no—
116#1294—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11C4×D412yes—
123C23×C11C2×SD1611yescharacteristic
124C23×C11C2×Q1611yescharacteristic
125C23×C11#13512yes—
126Q8×C11—42no—
127Q8×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11#9912yes—
159C2×C4×C11#10312yes—
160C2×C4×C11#10312yes—
161C2×C4×C11C2×C4211yescharacteristic
162C2×C4×C11#11711yescharacteristic
163C2×C4×C11C4×D412yes—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—82no—
168C2×Dic11—82no—
169C2×Dic11—82no—
170C2×Dic11—82no—
171C11⋊C8—44no—
172C2×C22⋊Q8C2×D1111yescharacteristic
173C2×C4×Q8Dic1111yescharacteristic, complemented
174C22×C42C2×D1111yescharacteristic
175C2×C22⋊C8—112no—
176C2×C4×C8—221no—
177#391Dic1111yescharacteristic, complemented
178#389Dic1111yescharacteristic, complemented
179#387—21no—
180#385—21no—
181#380C2×D1111yescharacteristic
182C4×C4⋊C4—21no—
183C4×C4⋊C4Dic1111yescharacteristic, complemented
184C4×C22⋊C4—21no—
185C2×#95—112no—
186C2×#95—221no—
187C2×#95—221no—
188#336—221no—
189#328—118no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—22no—
198C22×C11C4×C22⋊C411yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C22×C11#41011yescharacteristic
201C22×C11C2×#10311yescharacteristic
202C22×C11#41611yescharacteristic
203C22×C11#42111yescharacteristic
204C22×C11#42111yescharacteristic
205C22×C11C4×SD1612yes—
206C22×C11C4×Q1612yes—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—41no—
216C4×C11—81no—
217C4×C11—81no—
218Dic11—84no—
219C22×Q8C2×Dic1111yescharacteristic
220C23×C4—222no—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22×D1111yescharacteristic
224C22×C8—222no—
225C22⋊Q8—22no—
226C22⋊Q8C4×D1114yes—
227C4×Q8—42no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×Dic1111yescharacteristic
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C4⋊C4C2×Dic1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42—42no—
239C2×C42C2×Dic1111yescharacteristic
240C2×C42C2×Dic1111yescharacteristic
241C2×C42C22⋊D1111yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C22⋊C8—114no—
244C22⋊C8—222no—
245C4×C8—442no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—114no—
252#95—222no—
253#95—442no—
254#95—442no—
255C2×C11—22no—
256C2×C11—22no—
257C2×C11#151611yescharacteristic
258C2×C11#151811yescharacteristic
259C2×C11#152011yescharacteristic
260C2×C11#152111yescharacteristic
261C2×C11C4×#9911yescharacteristic
262C2×C11#175911yescharacteristic
263C2×C11C4×#10311yescharacteristic
264C24C2×C22⋊D1111yescharacteristic
265C2×Q8—21no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8C4×Dic1112yes—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—224no—
281C22×C4—442no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4#432512yes—
288C22×C4#432612yes—
289C22×C4C22⋊Dic1111yescharacteristic
290C22×C4C22⋊Dic1111yescharacteristic
291C22×C4C22⋊Dic1111yescharacteristic
292C22×C4C22⋊Dic1111yescharacteristic
293C22×C4C2×C4×D1112yes—
294C22×C4#433912yes—
295C22×C4C22×Dic1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297C2×C8—224no—
298C2×C8—442no—
299C2×C8—442no—
300C4⋊C4—21no—
301C4⋊C4—24no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4C4×Dic1112yes—
307C22⋊C4—24no—
308C22⋊C4—42no—
309C42—22no—
310C42—22no—
311C42—41no—
312C42—41no—
313C42—42no—
314C42—42no—
315C11#822111yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C4×C22⋊D1112yes—
321C23C2×#432511yescharacteristic
322C23C2×#432611yescharacteristic
323C23#6700312yes—
324C23C2×C22⋊Dic1111yescharacteristic
325Q8—42no—
326Q8—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6689812yes—
365C2×C4#6689912yes—
366C2×C4#6689912yes—
367C2×C4C2×C4×Dic1111yescharacteristic
368C2×C4#6697911yescharacteristic
369C2×C4C4×C22⋊D1112yes—
370C8—444no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22C4×#432512yes—
380C22C4×#432612yes—
381C22C4×C22⋊Dic1111yescharacteristic
382C22C2×#6689811yescharacteristic
383C22C2×#6689911yescharacteristic
384C22#1062284611yescharacteristic
385C22#1062284911yescharacteristic
386C22#1062284911yescharacteristic
387C22#1062285311yescharacteristic
388C4—22no—
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—42no—
396C4—41no—
397C4—81no—
398C4—81no—
399C4—884no—
400C2—22no—
401C2—22no—
402C2#1306717211yescharacteristic
403C2#1306718011yescharacteristic
404C2#1306718811yescharacteristic
405C2#1306719311yescharacteristic
406C2C4×#6689811yescharacteristic
407C2#1306842611yescharacteristic
408C2C4×#6689911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11#8221
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
7. C2×C4×Q8×C11C4semidirect
9. C11×#391C4semidirect
10. C11×#389C4semidirect
15. C4×C11×C4⋊C4C4semidirect
22. #10622176C4semidirect
173. C2×C4×Q8Dic11semidirect
177. #391Dic11semidirect
178. #389Dic11semidirect
183. C4×C4⋊C4Dic11semidirect
315. C11#8221semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×C22⋊(C11⋊C8)2
C2×#106221762
#130668432
#130664942
C4×C11×C22⋊Q82
#822111